Differentially private sliced inverse regression in the federated paradigm

We extend the celebrated sliced inverse regression to address the challenges of decentralized data, prioritizing privacy and communication efficiency. Our approach, federated sliced inverse regression (FSIR), facilitates collaborative estimation of the sufficient dimension reduction subspace among multiple clients, solely sharing local estimates to protect sensitive datasets from exposure. To guard against potential adversary attacks, FSIR further employs diverse perturbation strategies, including a novel multivariate Gaussian mechanism that guarantees differential privacy at a low cost of statistical accuracy. Additionally, FSIR naturally incorporates a collaborative variable screening step, enabling effective handling of high-dimensional client data. Theoretical properties of FSIR are established for both low-dimensional and high-dimensional settings, supported by extensive numerical experiments and real data analysis.